show that root3 is irrtional
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The number √3 is irrational ,it cannot be expressed as a ratio of integers a and b. To prove that this statement is true, let us Assume that it is rational and then prove it
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Given:
To find:
is an irrational number.
Solution:
(Were p and q is a co-prime)
Squaring both the side in above equation
if 3 is a factor of
Then, 3 will also be a factor of p
{where m is a integer}
Squaring both sides we get
Substitute the value of in the equation
If 3 is a factor of
Then, 3 will also be factor of q
Hence, 3 is a factor of p & q both
So, our assumption that p & q are co-prime is wrong.
So, is an "irrational number". Hence proved.
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